Four different topics have been studied under this project: (a) (Eisenberg, Hill, Chen). Isometric transient and steady contraction properties have been calculated from a self-consistent theoretical model of muscle contraction. Agreement with experiment is very good. Recent biochemical results, however, compel us to extend the model to eight states (four attached, four unattached). We are presently engaged in adjustment of model parameters to obtain the best possible fit with experimental data. The unique feature of this work is the bridge we are building between muscle biochemistry and muscle biophysics. (b) (Hill, Eisenberg, Chalovich). In preparation for future extension of the above model to the regulation of muscle contraction by Ca ions, we have developed a model for the cooperative steady-state ATPase activity of myosin subfragment-1 on actin-troponin-tropomyosin. Experiments (by Chalovich and Eisenberg) are in progress that will be compared with the theory. (c) (Hill). A much more detailed account has been published on the thermodynamic and kinetic interrelationships between the four main membrane systems of mitochondrial oxidative phosphorylation: respiratory chain; reverse ATPase, ADP-ATP exchange, and H ion, Pi symport. Also this treatment has been extended in two ways: the tight coupling assumed between the two subforces and subfluxes for each of the four systems has been relaxed to allow for the experimentally indicated incomplete coupling (inefficiency); and the four systems in the model have been extended to eight, to allow for H ion leak, Ca ions leak, Ca ions-H ion exchange; and ATP consumption in various processes within the mitochondrial matrix. (d) (Hill, Stein). A comprehensive theoretical study has been made of the cooperative properties of a lattice of interacting three-state enzyme molecules. Also we have examined the limits of the validity of the assumption, in biochemical kinetics, that the discrete states of a biochemical cycle, operating at steady state, are themselves separately in an internal equilibrium among substates.